he the Module 12 Concept Questions Version 2.0 January 2012 3) [12.2] Circles an

Question

he the Module 12 Concept Questions Version 2.0 January 2012 3) [12.2] Circles and completing the square. The equation of a circle with center (h, k) and radius r can be written as (x--h)" + (y-k)2 = r2. When an equationof a clrcle that not in this form is encountered, "completing the square" is used to rewrite it in this form. a) The equation of a circle is given as x2-4x y2 + 6y 12. Use "completing the square" to rewrite this equation as follows: i) Add a number to both sides to make x2-4x a perfect square. i) Now, add a number to both sides of your equation from (i) to make y2 + 6y a perfect square ii) Write the equation in the form (x -h)2 (y - k)2r2. b) State the center and radius of the circle. Your instructor will complete the following. Your work on these questions demonstrates mastery. these questions should he improved. Redo these problems:

Explanation / Answer

1) x^2 - 4x + y^2 + 6y = 12

i) to make x^2 - 4x a perfect square we add 4 on both sides

( x^2 - 4x + 4 ) + y^2 + 6y = 12 + 4

ii) to make y^2 + 6y a perfect square we add 9 on both sides

( x^2 - 4x + 4 ) + (y^2 + 6y+9) = 12 + 4 + 9

iii)nwriting equation in standard form  

( x - 2 )^2 + ( y + 3 )^2 = 25

b) radius = 5

center = ( 2 , -3 )

Related Questions

Navigate

• Browse (All)
• Browse H
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.